Will the reaction described by the equation [latex]CO(g, 0.010\ bar) + 2\ H_{2}(g, 0.010\ bar) → CH_{3}OH(l)[/latex] occur spontaneously at 25°C?

We first use Table 23.1 to calculate [latex]ΔG^{\circ}_{rxn}[/latex] : [latex]ΔG^{\circ}_{rxn} = ΔG^{\circ}_{f}[CH_{3}OH(l)] – ΔG^{\circ}_{f}[CO(g)] –2\ ΔG^{\circ}_{f}[H_{2}(g)] \\=(1)(–166.6\ kJ·mol^{–1}) – (1)(–137.2\ kJ·mol^{–1}) –(2)(0\ kJ·mol^{–1}) \\= –29.4\ kJ·mol^{–1}[/latex] The negative value of [latex]ΔG^{\circ}_{rxn}[/latex] means that the reaction described by the equation [latex]CO(g, 1\ bar) + 2\ H_{2}(g, 1\ bar) → CH_{3}OH(l)[/latex] proceeds spontaneously at standard conditions. However, it does not tell us whether the reaction will occur when the pressures of [latex]CO(g)[/latex] and [latex]H_{2}(g)[/latex] both are 0.010 bar, as originally stated. To find out, we must use Equation 23.20 to calculate [latex]ΔG_{rxn}[/latex]: [latex]ΔG_{rxn} =ΔG^{\circ}_{rxn}+ RT\ ln\ Q \\ = –29.4\ kJ·mol^{–1} + (8.3145\ J·K^{–1}·mol^{–1})(298\ K)ln\left(\frac{1}{(0.010)(0.010)^2 } \right) \\=–29.4\ kJ·mol^{–1} + 34.2\ kJ·mol^{–1} = +4.8\ kJ·mol^{–1}[/latex] Because [latex]ΔG_{rxn} \gt 0[/latex] , the reaction will not occur spontaneously if the pressures of [latex]CO(g)[/latex] and [latex]H_{2}(g)[/latex] are 0.010 bar, even though the reaction is spontaneous at standard conditions.

Question 23.10: Will the reaction described by the equation CO(g, 0.010 bar)......

General Chemistry [1096620]

Will the reaction described by the equation

CO(g, 0.010\ bar) + 2\ H_{2}(g, 0.010\ bar) → CH_{3}OH(l)

occur spontaneously at 25°C?

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

We first use Table 23.1 to calculate $ΔG^{\circ}_{rxn}$ :

ΔG^{\circ}_{rxn} = ΔG^{\circ}_{f}[CH_{3}OH(l)] – ΔG^{\circ}_{f}[CO(g)] –2\ ΔG^{\circ}_{f}[H_{2}(g)] \\=(1)(–166.6\ kJ·mol^{–1}) – (1)(–137.2\ kJ·mol^{–1}) –(2)(0\ kJ·mol^{–1}) \\= –29.4\ kJ·mol^{–1}

The negative value of $ΔG^{\circ}_{rxn}$ means that the reaction described by the equation

CO(g, 1\ bar) + 2\ H_{2}(g, 1\ bar) → CH_{3}OH(l)

proceeds spontaneously at standard conditions. However, it does not tell us whether the reaction will occur when the pressures of $CO(g)$ and $H_{2}(g)$ both are 0.010 bar, as originally stated. To find out, we must use Equation 23.20 to calculate $ΔG_{rxn}$ :

ΔG_{rxn} =ΔG^{\circ}_{rxn}+ RT\ ln\ Q \\ = –29.4\ kJ·mol^{–1} + (8.3145\ J·K^{–1}·mol^{–1})(298\ K)ln\left(\frac{1}{(0.010)(0.010)^2 } \right) \\=–29.4\ kJ·mol^{–1} + 34.2\ kJ·mol^{–1} = +4.8\ kJ·mol^{–1}

Because $ΔG_{rxn} \gt 0$ , the reaction will not occur spontaneously if the pressures of $CO(g)$ and $H_{2}(g)$ are 0.010 bar, even though the reaction is spontaneous at standard conditions.

TABLE 23.1 Standard molar entropies (S°), enthalpies of formation $(\Delta H^{\circ}_{f} )$ , and Gibbs energies of formation $(\Delta G^{\circ}_{f} )$ of various substances at 25°C and one bar (see also Appendix D)*
Substance	$S^{\circ}/J\cdot K^{−1}\cdot mol^{−1}$	$\Delta H^{\circ}_{f}/kJ\cdot mol^{-1}$	$\Delta G^{\circ}_{f}/kJ\cdot mol^{-1}$	Substance	$S^{\circ}/J\cdot K^{−1}\cdot mol^{−1}$	$\Delta H^{\circ}_{f}/kJ\cdot mol^{-1}$	$\Delta G^{\circ}_{f}/kJ\cdot mol^{-1}$
$Ag(s)$	42.6	0	0	$H_{2}O_{2}(l)$	109.6	–187.8	–120.4
$AgCl(s)$	96.3	–127.0	–109.8	$H_{2}S(g)$	205.8	–20.6	–33.4
$C(s,\ diamond)$	2.4	1.9	2.9	$N(g)$	153.3	472.7	455.5
$C(s,\ graphite)$	5.7	0	0	$N_2(g)$	191.6	0	0
$CH_{4}(g)$	186.3	–74.6	–50.5	$NH_{3}(g)$	192.8	–45.9	–16.4
$C_{2}H_{2}(g)$	200.9	227.4	209.9	$N_{2}H_{4}(l )$	121.2	50.6	149.3
$C_{2}H_{4}(g)$	219.3	52.4	68.4	$NO(g)$	210.8	91.3	87.6
$C_{6}H_{6}(l)$	173.4	49.1	124.5	$NO_{2}(g)$	240.1	33.2	51.3
$CH_{3}OH(l )$	126.8	–239.2	–166.6	$N_{2}O(g)$	220.0	81.6	103.7
$CH_{3}Cl(g)$	234.6	–81.9	–58.4	$N_{2}O_{4}(g)$	304.4	11.1	99.8
$CH_{3}Cl(l )$	145.3	–102	–51.5	$N_{2}O_{5}(s)$	178.2	–43.1	113.9
$CH_{2}Cl_{2}(g)$	270.2	–95.4	–68.8	$Na(g)$	153.7	107.5	77.0
$CH_{2}Cl_{2}(l )$	177.8	–124.2	–70.0	$Na(s)$	51.3	0	0
$CHCl_{3}(g)$	295.7	–102.7	6.0	$O(g)$	161.1	249.2	231.7
$CHCl_{3}(l)$	201.7	–134.1	–73.7	$O_{2}(g)$	205.2	0	0
$CO(g)$	197.7	–110.5	–137.2	$P(s, white)$	41.1	0	0
$CO_{2}(g)$	213.8	–393.5	–394.4	$P(s, red)$	22.8	–17.6	–12.1
$Cl(g)$	165.2	121.3	105.3	$PCl_3(g)$	311.8	–287.0	–267.8
$Cl_{2}(g)$	223.1	0	0	$PCl_5(g)$	364.6	–374.9	–305.0
$H(g)$	114.7	218.0	203.3	$S(s, rhombic)$	28.5	0	0
$H_{2}(g)$	130.7	0	0	$S(s, monoclinic)$	32.6	0.3	0.1
$H_{2}O(g)$	188.8	–241.8	–228.6	$SO_{2}(g)$	248.2	–296.8	–300.1
$H_{2}O(l)$	70.0	–285.8	–237.1	$SO_{3}(g)$	256.8	–395.7	–371.1
*Most data from CRC Handbook of Chemistry and Physics, 87th Online Edition, 2006–2007.